inertia Module¶
- combine_bike_rider(bicyclePar, riderPar)¶
Combines the inertia of the bicycle frame with the inertia of a rider.
- Parameters:
- bicyclePardictionary
The benchmark parameter set of a bicycle.
- riderPardictionary
The rider’s mass, center of mass, and inertia expressed in the benchmark bicycle reference frame.
- Returns:
- bicyclePardictionary
The benchmark bicycle parameters with a rigid rider added to the bicycle frame.
- compound_pendulum_inertia(m, g, l, T)¶
Returns the moment of inertia for an object hung as a compound pendulum.
- Parameters:
- mfloat
Mass of the pendulum.
- gfloat
Acceration due to gravity.
- lfloat
Length of the pendulum.
- Tfloat
The period of oscillation.
- Returns:
- Ifloat
Moment of interia of the pendulum.
- inertia_components(jay, beta)¶
Returns the 2D orthogonal inertia tensor.
When at least three moments of inertia and their axes orientations are known relative to a common inertial frame of a planar object, the orthoganl moments of inertia relative the frame are computed.
- Parameters:
- jayndarray, shape(n,)
An array of at least three moments of inertia. (n >= 3)
- betandarray, shape(n,)
An array of orientation angles corresponding to the moments of inertia in jay.
- Returns:
- eyendarray, shape(3,)
Ixx, Ixz, Izz
- parallel_axis(Ic, m, d)¶
Returns the moment of inertia of a body about a different point.
- Parameters:
- Icndarray, shape(3,3)
The moment of inertia about the center of mass of the body with respect to an orthogonal coordinate system.
- mfloat
The mass of the body.
- dndarray, shape(3,)
The distances along the three ordinates that located the new point relative to the center of mass of the body.
- Returns:
- Indarray, shape(3,3)
The moment of inertia about of the body about a point located by d.
- part_inertia_tensor(par, part)¶
Returns an inertia tensor for a particular part for the benchmark parameter set.
- Parameters:
- pardictionary
Complete Benchmark parameter set.
- partstring
Either ‘B’, ‘H’, ‘F’, ‘R’, ‘G’, ‘S’, ‘D’
- Returns:
- Indarray, shape(3,3)
Inertia tensor for the part.
Notes
Parts G, S, and D are additional parts not included in the published paper on the benchmark bicycle, they are only relavant if used. See the documentation.
- principal_axes(I)¶
Returns the principal moments of inertia and the orientation.
- Parameters:
- Indarray, shape(3,3)
An inertia tensor.
- Returns:
- Ipndarray, shape(3,)
The principal moments of inertia. This is sorted smallest to largest.
- Cndarray, shape(3,3)
The rotation matrix.
- rotate_inertia_tensor(I, angle)¶
Returns inertia tensor rotated through angle. Only for 2D
- tor_inertia(k, T)¶
Calculate the moment of inertia for an ideal torsional pendulm
- Parameters:
- k: torsional stiffness
- T: period
- Returns:
- I: moment of inertia
- torsional_pendulum_stiffness(I, T)¶
Calculate the stiffness of a torsional pendulum with a known moment of inertia.
- Parameters:
- Imoment of inertia
- Tperiod
- Returns:
- kstiffness
- tube_inertia(l, m, ro, ri)¶
Calculate the moment of inertia for a tube (or rod) where the x axis is aligned with the tube’s axis.
- Parameters:
- lfloat
The length of the tube.
- mfloat
The mass of the tube.
- rofloat
The outer radius of the tube.
- rifloat
The inner radius of the tube. Set this to zero if it is a rod instead of a tube.
- Returns:
- Ixfloat
Moment of inertia about tube axis.
- Iy, Izfloat
Moment of inertia about normal axis.